• The Pure and Applied Mathematics
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• v.23 no.3
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• pp.287-307
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• 2016

Using the fixed point method, we prove the Hyers-Ulam stability of an additive-quadratic-cubic-quartic functional equation in matrix fuzzy normed spaces.

• The Pure and Applied Mathematics
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• v.6 no.1
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• pp.1-8
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• 1999

Let $K_{\alpha}(G)$ (resp. $K_s(G)$) be the abelian (resp. symmetric) Kac algebra for a locally compact group G. We show that there exists a one-to-one correspondence between the subgroups of G and the sub-Kac algebras of $K_{\alpha}(G)$ (resp. $K_s(G)$). Moreover we obtain similar correspondences between the subgroups of G and the reduced Kac algebras of $K_{\alpha}(G)$ (resp. $K_s(G)$).

• The Pure and Applied Mathematics
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• v.22 no.4
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• pp.383-387
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• 2015

In [1], the definition of C*-Lie ternary (σ,τ,ξ)-derivation is not well-defined and so the results of [1, Section 4] on C*-Lie ternary (σ,τ,ξ)-derivations should be corrected.

• The Pure and Applied Mathematics
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• v.14 no.2 s.36
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• pp.111-125
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• 2007

For an odd mapping, we study a generalized additive functional equation in Banach spaces and Banach modules over a $C^*-algebra$. And we obtain generalized solutions of a generalized additive functional equation and so generalize the Cauchy-Rassias stability.

• Bulletin of the Korean Chemical Society
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• v.15 no.7
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• pp.568-571
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• 1994

Streptmyces fradiae NRRL B1195 and Streptomyces kanamyceticus IFO 13414 are highly resistant to the antibiotics they produce. The ribosomes of these organisms are found to be susceptible to the antibiotics, but the cell free extract of S fradiae is found to contain a phosphotransferase and an acetyltransferase which inactivate kanamycin and neomycin, and that of S. kanamyceticus an acetyltransferse which inactivates kanamycin and neomycin. The resistance of these organisms against streptomycin is found to be due to the resistant ribosomes; actually streptomycin activates their ribosomal systems for the synthesis of polyphenylalanine.

• The Pure and Applied Mathematics
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• v.28 no.2
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• pp.91-102
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• 2021

In this paper, we introduce Lie bracket Jordan derivations in Banach Jordan algebras. Using the direct method and the fixed point method, we prove the Hyers-Ulam stability of Lie bracket Jordan derivations in complex Banach Jordan algebras.

• The Pure and Applied Mathematics
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• v.29 no.4
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• pp.401-419
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• 2022

In this paper, we introduce the notion of partial S-metric space and prove a common fixed point theorem in the respective setting. An example is presented to show the effectiveness of this approach.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.1
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• pp.49-57
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• 2010

It is shown that for a derivation $$f(x_1{\cdots}x_{j-1}x_jx_{j+1}{\cdots}x_k)=\sum_{j=1}^{k}x_{1}{\cdots}x_{j-1}x_{j+1}{\cdots}x_kf(x_j)$$ on a unital $C^*$-algebra $\mathcal{B}$, there exists a unique $\mathbb{C}$-linear *-derivation $D:{\mathcal{B}}{\rightarrow}{\mathcal{B}}$ near the derivation, by using the Hyers-Ulam-Rassias stability of functional equations. The concept of Hyers-Ulam-Rassias stability originated from the Th.M. Rassias' stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.

• The Pure and Applied Mathematics
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• v.17 no.1
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• pp.65-80
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• 2010

In [17, 18], the fuzzy stability problems for the Cauchy additive functional equation and the Jensen additive functional equation in fuzzy Banach spaces have been investigated. In this paper, we prove the generalized Hyers-Ulam stability of the following quadratic functional equations in fuzzy Banach spaces: (0.1) f(x + y) + f(x - y) = 2f(x) + 2f(y), (0.2) f(ax + by) + f(ax - by) = $2a^2 f(x)\;+\;2b^2f(y)$ for nonzero real numbers a, b with $a\;{\neq}\;{\pm}1$.

• Journal of The Korean Society of Grassland and Forage Science
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• v.19 no.1
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• pp.49-56
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• 1999

With ${15}^N$ labeling under split roots system of winter rye (Secale cereale L.) and forage rape (Brassica napus L.) grown at $5^{\circ}C$ and $25^{\circ}C$, the N flows were respectively quantified to investigate the transport of newly absorbed nitrate-N in whole plant level at low temperature. Comparing with $25^{\circ}C$ culture condition, the total absorbed nitrate-N content at $5^{\circ}C$ decreased to 59.3% and 27.1% in winter rye and forage rape during 9 days. About 2.5% and 7.6 % of nitrate-N were transported into roots, respectively, in winter rye and in forage rape at $25^{\circ}C$. These proportions increased at $5^{\circ}C$ to 3.8% and 10.9%, respectively. Total N contents transferred by xylem in winter rye grown and forage rape grown at $25^{\circ}C$ during were 55.9 and 54.4 mg N/plant, respectively. xylem flows at $5^{\circ}C$ were 60.4% and 28.8% lower than at $25^{\circ}C$ for winter rye and forage rape. These valves represented that averagely 96.8 % and 90.8% of total absorbed nitrate-N were transferred to leaves in winter rye and forage rape during 9 days. Phloem flows were the smallest among other N flows and were much less influenced by temperature treatment for two species examined. About 2.5% and 0.5% of absorbed N were recycled into roots by phloem transport at $25^{\circ}C$, respectively, for winter rye and forage rape. These proportions increased to 5.2% and 0.9% at $5^{\circ}C$.